In a small bowl, combine steak, soy sauce, oyster sauce, and sugar. Cover and let marinate for several minutes. If you have time, refrigerate and marinate 4-8 hours.
Heat a large wok over medium-high heat for several minutes. Add 1 tablespoon of peanut oil and heat for several minutes. Add broccoli and cook for 1 minute, stirring occasionally. Season with salt and cook for 1 minute more.
Add 1-2 tablespoons of water to create a steaming effect. Cook for 2-3 minutes more, until water is absorbed and broccoli is bright green and tender. Remove from heat and pour broccoli into a large serving dish. Set aside.
Return wok to stove. Add 1/2 tablespoon of peanut oil and heat for several minutes. Add marinated steak and cook, stirring occasionally, until steak is brown and no pink remains on the outside. For a well-done steak, cook for about 3-4 minutes. Remove from heat and pour steak and sauce on top of dish with broccoli. Serve immediately with cooked rice.
Cooks' note: You can cut down on sodium by opting for reduced sodium soy sauce.